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Flashcards: Translating Words to Absolute Values

A supermarket features a guessing game in which customers try to guess the number of jelly beans in a jar, and those whose guess is within 5 jellybeans of the actual number win a prize. Which of the following expressions represents the guesses, , that would win a prize if the exact number of jellybeans is 232?

$\left | G+232 \right |\leq 5$

$\left | G-5 \right |\leq 232$

$\left | G-232 \right |\leq 5$

$\left | G+5 \right |\leq 232$

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Flashcards: Translating Words to Absolute Values

Your answer:

$\left | G+232 \right |\leq 5$

Your answer:

$\left | G-5 \right |\leq 232$

Your answer:

$\left | G+5 \right |\leq 232$

Correct answer:

$\left | G-232 \right |\leq 5$

Explanation:

A helpful strategy on problems that ask you to convert a situation to an absolute value is to pick numbers that would work and then test the answer choices. Here if you were using numbers and not variables and absolute values this isn't that hard a problem: in order to win, you need to guess between 227 and 237 so that your number is within 5 of the total of 232. So you want an absolute value that will work for both 227 and 237. if you then test the answer choices you should see that the correct answer, $\left | G-232 \right |\leq 5$ , gives you the right boundaries for winning:

Flashcards: Translating Words to Absolute Values

On a television game show, contestants are asked to guess the price of an item, and the contestant whose guess is closest to the exact price wins that item. One item on the show was a microwave oven for which the exact price is $112, and Josh's guess was $6 away from that exact price. If Josh's guess can be represented by the variable , which of the following equations represents the amount that Josh guessed?

$\left | 6-j \right |=112$

$\left | j-112 \right |=6$

$\left | j-6 \right |=112$

$\left | 112-6 \right |=j$

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Flashcards: Translating Words to Absolute Values

Your answer:

$\left | 6-j \right |=112$

Your answer:

$\left | j-6 \right |=112$

Your answer:

$\left | 112-6 \right |=j$

Correct answer:

$\left | j-112 \right |=6$

Explanation:

Translating word problems to absolute values can be tricky, but in a multiple choice format you have a great opportunity to use process of elimination. Here the wording should lead you to a pretty good understanding of the actual numbers involved in the scenario: Josh's guess was $6 off of the correct value of $112, so he must have guessed either $106 or $118. So you can plug in those values for and see which answer choices match with both of those values. Among the answer choices:

$\left | j-112 \right |=6$ works. 118-112 = 6 and 106-112 = -6, for which the absolute value is 6.

$\left | j-6 \right |=112$ does not work. 118-6 does equal 112, but 106-6 = 100, for which the absolute value is not 112.

$\left | 112-6 \right |=j$ does not work. 112-6 does equal 106, but it does not equal 118 (or -118) so this equation doesn't account for both possibilities.

$\left | 6-j \right |=112$ does not work. 6-106 = -100, so the absolute value does not match 112.

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Flashcards: Translating Words to Absolute Values

Flashcards: Translating Words to Absolute Values

Flashcards: Translating Words to Absolute Values

Flashcards: Translating Words to Absolute Values

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All SAT Mathematics Resources

Flashcards: Translating Words to Absolute Values

Flashcards: Translating Words to Absolute Values

Flashcards: Translating Words to Absolute Values

Flashcards: Translating Words to Absolute Values

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DMCA Complaint

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Complaint Details

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